Question

If in the experiment, m1 is 38 g, m2 is 63 g, and m3 is 58 g, "and m3 remains static, what is the tension in the string connecting m1 and m3?"

Answer 1

Let's call a the acceleration of the system. The problem says that the block m3 is static, so the acceleration is zero: a=0.
Calling $T_1$ the tension of the string between m1 and m3, and $T_2$ the tension of the string between m2 and m3, the problem can be solved by writing the following system of equations:
$m_1 g-T_1=m1_a$
$T_1-T_2=m_3 a$
$T_2-m_2g=m_2a$
However, we know that a=0 and the problem asks only for $T_1$, so we just need to solve the first equation:
$m_1 g -T_1 =0$
and so
$T_1=m_1g=0.038~kg \cdot 9.81~m/s^2 = 0.37~N$